Electronic scattering, focusing, and resonance by a spherical barrier in Weyl semimetals

Abstract

We solve the Weyl electron scattered by a spherical step potential barrier. Tuning the incident energy and the potential radius, one can enter both quasiclassical and quantum regimes. Transport features related to far-field currents and integrated cross sections are studied to reveal the preferred forward scattering. In the quasiclassical regime, a strong focusing effect along the incident spherical axis is found in addition to optical caustic patterns. In the quantum regime, at energies of successive angular momentum resonances, a polar aggregation of electron density is found inside the potential. The findings will be useful in transport studies and electronic lens applications in Weyl systems.

Optimizing Dirac fermions quasi-confinement by potential smoothness engineering

“…These exotic properties of graphene Dirac fermions led to a plethora of electron-optics proposals and realizations, such as electronic optical fibers [7][8][9][10], lenses [11][12][13][14][15][16][17] and their advanced design to create highly focused electron beams [18], and even the combination of different optical elements to create a scanning Dirac fermions microscope [19]. Aside guiding, the partial reflection encountered at p-n interfaces has been proposed in the early days of graphene to create Fabry-Pérot interferometers with graphene n-p-n junctions [20].…”

Imaging Dirac fermions flow through a circular Veselago lens

“…Using this negative refraction, invisibility cloak has been realized for microwave photons [5], and perfect electromagnetic lenses have been proposed [6]. The possibility of forming such Veselago lenses using p-n junctions in graphene [7,8] as well as the resulting caustics [9][10][11][12][13][14][15] have attracted a lot of attention from a theoretical point of view. Recent works suggested that Veselago lensing could be used to create highly focused electron beams [16], and even a two-dimensional scanning Dirac fermions microscope [17].…”

“…The present study also reveals the existence of low current density points away from a smooth circular p-n junction, highly sensitive to the junction smoothness. While many studies investigated caustics of Veselago lenses [9][10][11][12][13][14][15]…”

Gradient-index electron optics in graphene pn junctions

“…The possibility to manipulate electron beams in graphene by means of pn junctions or elastic deformations has lead to various proposals for nano-electronic devices, such as Veselago lenses [4,6,[29][30][31][32][33][34][35], electron fiber optics [3,36], interferometers [37,38], valley beam splitters [7,26,[39][40][41][42][43][44][45][46][47][48][49][50], collimators [51,52], switches [53], reflectors [54,55], transistors [2,56,57], and Dirac fermions microscopes [58]. Electron optics has been extended recently from graphene to other materials, such as phosphorene where negative reflection has been pre-dicted [59,60], non-coplanar refraction and Veselago lenses in Weyl semi-metals [61][62][63][64], anomalous caustics in borophene pn junctions [65], and super-diverging lenses in Dirac materials [30].…”